Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#405 | C2 | semidirect |
| 3. C2×#88062 | C2 | semidirect |
| 6. #11718142 | C2 | semidirect |
| 7. #11718124 | C2 | semidirect |
| 21. #88050 | C4 | semidirect |
| 22. #88050 | C4 | semidirect |
| 23. #88049 | C4 | semidirect |
| 24. #88049 | C4 | semidirect |
| 88. #405 | D13 | semidirect |
| 160. C13 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#405 | 2 |
| C2×#88065 | 2 |
| C2×#88062 | 2 |
| #11718771 | 2 |
| #11718663 | 2 |
| #11718142 | 2 |
| #11718124 | 2 |
| #1929 | 13 |